circle trouble. problem in first comment

Question

anonymous · Answer

attachment

anonymous · Answer

72 is the angle right?

phi · Answer

How many degrees in a circle?

anonymous · Answer

360 degrees

anonymous · Answer

SO the find the length of the arc you can use this rule:

anonymous · Answer

Angle/Total angle *2*pi*radius

phi · Answer

now set up a proportion

they tell you the circumference  (all the way round) is 75 inches
that means  75  is to 360  as unknown length is to 72 
$$ \frac{75}{360}=  \frac{x}{72} $$

phi · Answer

If the arc were 180º  it is (almost?) obvious that its length would be 1/2 the whole circle.

here the arc is 72/360  of the whole circle.

anonymous · Answer

You don't the radius but you have the circumference so we have to know the equation that enables us to find the radius which is: C=2*pi*r

75=2*pi*r

75/pi=2r

23.87=2r

23.87/2=r

r=11.94 inches

anonymous · Answer

Since you we found the radius you can just input it into the first equation which I showed you and then solve it